Probabilities of Compound Events Worksheets, Grade 7 (7.SP.C.8) – Free PDF + Answer Key

First page of the probabilities of compound events practice worksheet

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PDFs print on US Letter paper. Free for classroom and home use.

Step-by-step math videos on the Math With Mr DJ YouTube channel →

Key idea

Multiply the probabilities. Ask first: does the first event change the second? Independent events (coins, dice, with replacement) leave it unchanged. Without replacement, both the numerator and the denominator drop.

Sample problems

Two fair coins are flipped. Find P(both tails).
Find P(at least one head) for those two coins.
A die is rolled and a coin flipped. Find P(even number and tails).
From the bag, two marbles are drawn WITH replacement. Find P(both blue).

Common mistakes to watch for

Answered ½ by adding the probabilities, or ₁⁄₃ by listing only HH, HT and TT.
Added to get ₂⁄₃, or used ₁⁄₈ by counting 6 faces plus 2 sides as 8 outcomes. The outcomes multiply, not add.
Changed the second fraction anyway. With replacement the bag is restored, so nothing changes.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

Teach with the slides (about 15 minutes), or watch the video together.
Practice with the worksheet. Questions climb from fluency to application to reasoning.
Check understanding with the exit ticket, and send the homework home.
Mark with the answer key — each answer shows the steps and the most likely mistake.